## Functional analysis, holomorphy, and approximation theory: proceedings of the Seminário de Análise Funcional, Holomorfia e Teoria da Aproximação, Universidade Federal do Rio de Janeiro, Brazil, August 7-11, 1978 |

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### Contents

Ansetnil and An Example of a QuasiNormable Frechet | 1 |

Edward Beckenstein and Extending Nonarchimedean Norms on | 33 |

Mauro Bianchini SilvaHolomorphy Types Borel Trans | 55 |

Copyright | |

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approximation property arbitrary assume b.v. space Banach space barrelled bornological bounded sets bounded subset closed closure coform compact set compact subset complete contained continuous functions continuous linear Corollary CVq(x CVq(X,F defined Definition denote dense differential domain domain of holomorphy dual duality element equivalent espaces examples exists finite Frechet space function f given Hausdorff space Hence Hilbert space holomorphic functions holomorphy type homeomorphism I.e. space implies induced inductive limit infinite dimensional isomorphism JB-algebra Jordan algebras Lemma Let f Levi problem linear map linear subspace locally convex space Math metric neighbourhood norm nuclear open set open subset plurisubharmonic polynomials Proof Proposition prove pseudoconvex relatively compact Remark resp restriction result satisfies SC(F Schauder Schwartz Schwartz's a.p. semi-norm sequence space F subalgebra Theorem theory topological linear subspace uniformly vector space X,cp